Study of Specific Discharge Energy in WEDM and its Application

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Study of speciﬁc discharge energy in WEDM and its application

Y.S. Liao

a,

, Y.P. Yu

b

a_{Department of Mechanical Engineering, National Taiwan University 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan} b_{Department of Mechanical Engineering, Hwa-Hsia College of Technology and Commerce, No. 111, Huashin Street, Junghe City,}

Taipei 235, Taiwan

Received 30 September 2003; received in revised form 7 April 2004; accepted 22 April 2004

Abstract

The relationship between machining parameters and machining characteristics of different materials in WEDM is difficult to obtain because a large number of experiments must be conducted repeatedly. A new concept attempting to solve this problem is presented in this paper. The specific discharge energy (SDE) defining as the real energy required to remove a unit volume of material is proposed. The SDE is constant for a specific material. Experimental results reveal that the relative relationship of SDE between different materials is invariant as long as all materials are machined under the same machining conditions. It is also found that the materials having close value of SDE demonstrate very similar machining characteristics such as machining speed, discharge frequency, groove width and surface finish of the machined surface under the same machining conditions. This result can be applied for the determination of the settings of machining parameters of different materials. Furthermore, by dimensional analysis of SDE, a quantitative relationship between machining characteristics such as the material removal rate and the efficiency of material removal and machining parameters is derived.

Keywords: Wire electrical discharge machining; Process planning; Speciﬁc discharge energy; Discharge eﬃciency

1. Introduction

Different materials have different characteristics, including machining speed, surface roughness of the machined surface, groove width, discharge frequency, abnormal discharge ratio, under different machining conditions in WEDM. Different materials even when they are machined under the same machining con-ditions exhibit different machining characteristics. It is difficult to control and predict the machining char-acteristics in WEDM. There are very few studies on this subject so far. Almost all the studies concerned with material deal with the effect of electrode material on machinability in WEDM or die sinking EDM[1,2]. Levy and Maggi [3] have compared the influence of material properties of different steels on machining characteristics, but only qualitatively. The material

properties such as melting point, density, specific heat, thermal conductivity, yield strength, etc., all should affect machining characteristics. It is extremely difficult to conclude and pinpoint a concise and definite physi-cal quantity that can fully reflect the material proper-ties in WEDM, and use it to predict machining characteristics. In general, the material removal rate and machining characteristics during the WEDM pro-cess depend on the distribution of the energy supplied to the gap by the electrical current. Various thermal models proposed for EDM [4–7] show that the com-plexities and the stochastic nature of multiple dis-charges render difficulties in analyzing the process theoretically. Fromthe energy point of view, a quantity defining as the real energy required to remove a unit volume of a specific material in wire electrical discharge machining and coined (SDE) is proposed in the paper. The SDE should be constant for a given material, and it is considered as one of the material properties in WEDM. The SDEs of different materials are compared first in the paper. Materials having close values of SDE

_{Corresponding author. Tel.: +886-2-2362-6431; fax:} +886-2-2363-1755.

E-mail address: liaoys@ntu.edu.tw (Y.S. Liao).

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are selected, and their machining characteristics under identical machining conditions are evaluated and com-pared. A quantitative relationship between machining characteristics and machining parameters is obtained through dimensional analysis of SDE. Diﬀerent from previous studies that were limited to qualitative discus-sions, the derived relationship enables the behavior of WEDM to be understood more comprehensively.

2. Theory of speciﬁc discharge energy

In wire electrical discharge machining, a metal wire is used as the electrode and de-ionized solvent as the machining liquid. A speciﬁc electrical voltage is applied to both the electrode and workpiece. Once the gap between two electrodes is narrow enough, electrical dis-charge occurs. Material removal is accomplished

through the thermal functions caused by the discharge, including evaporation and melting, and the function of force, including discharge impact pressure and explos-ive force, which expel the melted residue. Since the dis-charge process is a complex one, it is susceptible to the effect of a number of factors. However, from the per-spective of discharge machining energy, each pulse dur-ing the discharge process is an output of energy. The energy distribution between the workpiece and wire electrode and the actual effective removal energy should be related to the distance between the wire elec-trode and workpiece, flushing pressure, conductivity of the machining liquid and discharge on time.

During wire electrical discharge machining, the dis-charge power is determined by the single disdis-charge energy multiplied by discharge frequency. In reality, the discharge on time (Ton) for the same machining

operation must remain constant in order to obtain uni-formgroove width and stable machining. Fig. 1 illus-trates the typical voltage and electrical current waves resulting fromthe pulse generator of the machine used in the experiment. The current produced by the pulse generator has an equilateral triangle shape. If the aver-age working voltaver-age is VD, then the single discharge

energy is given by the following equation:

DE¼ ð

pulse duration

vðsÞiðsÞds ¼ VDKTon2 ð1Þ

where K denotes the rising slope of the electrical cur-rent and it is one of the design parameters of the dis-charge power source. Its unit is A/ls. Diﬀerent machining conditions generate diﬀerent discharge fre-quencies. Let the discharge frequency be Fq, then the

discharge power (W) can be expressed as

W¼ FqDE ¼ FqKVDTon2 ð2Þ

Nomenclature Aon arc on time

Aoﬀ arc oﬀ time

c speciﬁc heat

D erosion diameter of single discharge DE single discharge energy

F table feed rate Fw ﬂushing pressure

Fq discharge frequency

G groove width H workpiece height k thermal conductivity

K rising slope of the electrical current r ratio of abnormal discharges to the total

discharges

Se erosion rate of single discharge

Sv servo voltage

Toﬀ discharge oﬀ time

Ton discharge on time

u0 speciﬁc discharge energy

VD average working voltage

W discharge power

W0 _{discharge power actually provided by the}

power supply

W00 _{eﬀective discharge power}

W

W power of single discharge Ws wire speed

g discharge eﬃciency q density

h average temperature generated on work-piece surface

h

h average temperature at single discharge instant

Fig. 1. Typical waveforms of voltage and current of a single discharge.

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For the machine used in the experiment, there are two sets of power parameters. Normal discharge time Ton and oﬀ time Toﬀ are used when the discharge is

normal. They are switched to Aon and Aoﬀ,

represent-ing abnormal discharge time and oﬀ time, respectively, when an abnormal discharge is detected. Other machining parameters include servo voltage Sv, wire

speed Ws and ﬂushing pressure. Not every discharge in

the actual machining process is a normal discharge. Some are arc discharges while others are short pulses. Let the ratio of abnormal discharges in the total dis-charges, called abnormal ratio thereafter, be denoted by r. Arc discharge, based on the experimental data, usually accounts for half of the abnormal discharges, short discharge does not provide any discharge energy, hence the discharge power actually provided by the power supply denoted by W0_is

W0¼ VDKFqðTon2 ð1 rÞ þ A2onðr=2ÞÞ ð3Þ

One part of the energy supplied by the power source is used to remove workpiece material, the other is transmitted to the wire electrode, and the rest is dis-tributed in the machining fluid. The effective energy that actually achieves workpiece removal accounts for part of the total energy, and it is related to the machin-ing parameters, electrode and work materials[8,9]. Let the proportion of the total energy that is actually used for metal removal be defined as discharge efficiency and denoted by g, then the effective discharge power W00_is

W00¼ W0_g _ð4Þ

The discharge efficiency is related to materials, machining parameters and condition of the machine. Defining the real energy needed to remove a unit vol-ume of material during the machining process as the specific discharge energy (SDE), denoted by u0, then

SDE can be expressed as

u0¼ W00 GHF ¼VDKFqðT 2 onð1 rÞ þ A2onðr=2ÞÞg GHF ð5Þ

where G is the groove width, H is the workpiece height, F is the table feed rate.

SDE should be constant for a given material irres-pective of machining conditions, and it can be considered as one of the properties of a material in wire-EDM. For a given work material, the discharge efficiency would be influenced by electrode material and machining parameters. By definition, it is readily understood that the larger the SDE the harder is material removal. The higher the discharge efficiency, the more is the energy distributed in workpiece during machining. Since SDE is a material property, it is expected that materials having equal SDE would result

in identical machining characteristics (machining speed, surface roughness of the machined surface, groove width, discharge frequency, abnormal discharge ratio) if they are machined by the same machining con-ditions.

Eq. (5) can also be derived fromdimensional analy-sis. Physically u0 should be constant for a given

material. All possible variables related to WEDM and their dimensions are listed inTable 1. The quantities hh and h are the instantaneous temperature at single dis-charge instant, and the average temperature generated on workpiece surface, respectively. Quantities k, q, c are the thermal conductivity, density and specific heat of work material. Similar to the traditional specific cut-ting energy in cutcut-ting [10], the average temperature on surface of workpiece should be influenced by u0 and

thermal properties of the material. Since material removal rate is related to machining speed and machin-ing groove. Through dimension analysis a dimension-less equation is obtained as follows:

h u0 kqc FG 1=2 ¼ C1 ð6Þ or u0 h kqc FG 1=2 ð7Þ

Considering the energy provided during wire electri-cal discharge machining, physielectri-cal quantities related to energy are speciﬁc discharge energy, eﬀective discharge power and temperature on the workpiece surface. Simi-larly, taking the workpiece height, where the energy or temperature is distributed on, into consideration,

Table 1

Dimension analysis of physical quantities

Physical quantity Symbol Dimension Speciﬁc discharge energy u0 FL2

Table feed rate F LT1

Average temperature generated on workpiece surface

h h

Average temperature at single discharge instant h h h Groove width G L Workpiece height H L Thermal conductivity k FLT1L1h1 Density q ML3 Speciﬁc heat c FLM1h1

Eﬀective discharge power W00 _FLT1 Power of single discharge _W_W FLT1 Erosion diameter of single

discharge

D L

Erosion rate of single discharge Se LT1 Temperature (h), length (L), time (T), mass (M), force (F).

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another dimensionless equation is obtained as follows: 1 h W0gu0 kqcH 1=2 ¼ C2 ð8Þ or h W 0_gu 0 kqcH 1=2 ð9Þ

Substituting Eq. (9) into Eq. (7) yields

u0

W0g

FGH ð10Þ

This is the same as the deﬁnition of speciﬁc discharge energy given previously in Eq. (5).

3. Experiment and analysis of results

The first goal of the experiment was to check if SDE is constant for a given material, and to verify if the machining characteristics are identical for the materials having equal value of SDE machined under the same machining conditions. The second purpose was to understand to what extent each machining parameter affects the discharge efficiency g. The experimental apparatus included a flushing type 5-axis CNC wire electrical discharge machine manufactured by Ching-Hong Inc., Taiwan. The main unit is equipped with an iso-energy discharge wave power supply systemthat generates triangular waves with equal slopes and a peak current slope of 450 A/ls. The average working voltage was 80 V. Machining parameters can be adjus-ted fromthe control panel. The wire electrode was 6–4 brass wire 60% (Cu), 40% (Zn) with a diameter of 0.25 mm. Its tensile strength was 95–105 kgf/mm2and the melting point was 930 v

C. Experiments were con-ducted under G95 mode. In others words, the servo voltage control was set in machining.

3.1. Speciﬁc discharge energy and its relationship with machining characteristics

According to Table 2, two sets of machining con-ditions were selected at ﬁrst, and four workpiece mate-rials were used, namely, aluminium (Al) alloy, titanium

(Ti) alloy, stainless steel, a cold work tool steel, and a hot work tool steel. Based on Eq. (5), the SDE of dif-ferent materials was calculated individually by assuming the discharge eﬃciency g was 1.0. The SDE of various materials under two sets of machining con-ditions are listed inTable 3. The values in brackets are values relative to the 6061 aluminium alloy. From

Table 3, it is noted that different values of SDE arise for each material under the two different machining conditions rather than just one value as postulated. The reason is that the discharge efficiency is different for the different machining conditions, but since it is unknown beforehand it was taken to be one in both cases. It is also noted that the relative relationship of SDE between different materials (i.e. the values given in the brackets) remains unchanged as machining con-ditions were the same for each one. This result also indirectly supports the postulation that the SDE for a given material should be constant.

The next experiment is to verify that the materials having the same SDE have identical machining char-acteristics if they were machined under the same machining conditions. Referring to Table 3, the two materials with similar SDE values, SKD11 and Inconel 718, were selected for this study. Their SDEs are 890 and 900 J/mm3, respectively. They were machined under the machining conditions given in Table 4. Workpieces with a thickness of 15 mm were used in all experiments. The other machining conditions include the ﬂushing pressure of 20 kg/cm2, wire speed of 8 m/min and wire tension of 900 gf. The resulting machining characteristics are summarized inTables 5–7. They are: the abnormal ratio, deﬁned as the proportion of abnor-mal discharges out of total discharges in a particular

Table 2

Experimental machining parameters Set no Machining parameter

Discharge on time (ls) Discharge oﬀ time (ls) Arc on time (ls)

Arc oﬀ time (ls) Servo voltage (V) 1 0.9 16 0.5 18 50 2 0.7 16 0.5 18 45

Other machining parameters: wire tension 1200 gf, wire speed 9 m/ min, ﬂushing pressure 20 kg/cm2.

Table 3

SDE of various materials (J/mm3)

Set no Al alloy 6061 Super alloy Inconel 718 Ti alloy Ti–6Al–4V Stainless steel SUS 304

Cold work tool steel SKD11

Hot work tool steel SKD61

1 275 (1) 900 (3.27) 690 (2.51) 840 (3.05) 890 (3.24) 980 (3.56) 2 225 (1) 730 (3.24) 563 (2.50) 690 (3.07) 735 (3.27) 813 (3.61) ( ) Relative to Al 6061 values.

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time interval, machining speed, discharge frequency, groove width and roughness of the machined surface. As it can be seen fromthe tables, the values of each of these machining characteristics are almost the same. This indicates that materials with similar SDE values exhibit very similar machining characteristics as long as they are machined under the same machining con-ditions. By this finding, it is concluded that, based on the evidence obtained so far, SDE postulated in paper can fully reflect the properties of a material in wire-EDM. One of the real applications of this finding is to include SDE as one of a machining parameter in con-structing the neural network model between machining parameters and machining characteristics. Prediction of the machining characteristics of different materials hav-ing different SDE can then be accomplished through the network. And once the neural network model is established, it can be applied for process planning. This work is beyond the scope of this paper and is not reported here.

3.2. Eﬀect of machining parameters on discharge eﬃciency

A different discharge efficiency arises for different machining conditions. After considering realistic machining conditions, all identified variables that may affect discharge efficiency were selected as the control factors in the experiment undertaken to investigate this fact. They are workpiece thickness, discharge on time, discharge off time, arc on time, arc off time, wire speed, flushing pressure and servo voltage. Because of the large number of control factors, the L18 mixed orthog-onal table of the Taguchi quality design method [11]

was adopted. The level settings for all factors in the experiment are listed in Table 8. The machining char-acteristics under study were: groove width, machining speed, discharge frequency, abnormal ratio, roughness of the machined surface, and discharge eﬃciency. It should be noted that the discharge eﬃciency for a machining condition is unknown in practice. Hence, for analysis purpose, the relative value with respect to a standard value was computed. In our case, the machining condition of Ton¼ 0:9 ls, Sv¼ 50 V was

taken as the standard. By considering the SDE for a material is constant, and the discharge efficiency equals 1 under the standard machining condition, the relative value of discharge efficiency under different machining condition can be computed. After conducting the experiments, the signal to noise (S/N) ratios were com-puted, and the analysis of variable was employed to find the significant factors affecting each machining characteristics. The results are given in Table 9. In

Table 5

Machining characteristics of SKD11 and Inconel 718 machined under the condition set no. 1

Machining characteristic Abnormal ratio Machining speed Spark frequency Groove width Surface roughness

Material SKD11 38 6.9 26.5 354 3.4

Inconel 718 37 6.8 26.5 349 3.2

Unit: abnormal ratio (%), machining speed (mm/min), spark frequency (kHz), groove width (lm), surface roughness (lm). Table 4

Experimental machining parameters Set no Machining parameter

Discharge on time (ls) Discharge oﬀ time (ls) Arc on time (ls) Arc oﬀ time (ls) Servo voltage (V) 1 0.9 16 0.5 18 50 2 0.9 16 0.5 18 40 3 0.7 16 0.5 18 40

Other machining parameter: wire tension 1200 gf, wire speed 9 m/ min, ﬂushing pressure 20 kg/cm2.

Table 7

Material SKD11 44 6.3 32.0 340 3.2

Inconel 718 42 6.2 31.5 335 3.0

Table 6

Material SKD11 45 8.2 32.0 349 3.7

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addition, the trends in the variations of machining characteristics with respect to each signiﬁcant machin-ing parameter plotted and were shown inTable 10.

Referring to Table 9, it is found that the discharge on time and servo voltage are the two most significant factors affecting the discharge efficiency g. The larger the discharge on time, the lower the discharge efficiency. Since the amount of input energy depends strongly on the discharge on time, this implies that given a high energy during the machining process, the percentage of effective energy that actually reaches the workpiece and removes the material declines signifi-cantly. A similar conclusion had also been reached pre-viously by others [12–15]. For the effect of servo voltage, a greater servo voltage results in lower dis-charge efficiency. The reason is that servo voltage reflects the distance between the wire electrode and workpiece. The shorter is this distance, the more likely

a higher percentage of eﬀective energy will achieve material removal. In other words, discharge eﬃciency is negatively correlated with the distance between the wire electrode and the workpiece.

4. Some applications of speciﬁc discharge energy The SDE can be brought to several applications. Machining characteristics in WEDM studied pre-viously such as groove width and surface roughness have been limited to qualitative discussions of the experimental results. In the following, a quantitative relationship between machining characteristics and machining parameters is obtained through SDE. The derived relationship enables an understanding of the behavior of WEDM more comprehensively, and can be applied for the future development of servo control strategy.

4.1. Estimation of machining groove width

A too large variation of the groove width will influ-ence the dimensional accuracy of machined workpiece. Therefore, machining parameters must be decided care-fully. From Table 9, it is concluded that workpiece height, discharge on time, arc on time and servo volt-age have a significant effect on the machined groove width. Among these, discharge on time and workpiece height are the most significant factors, while arc on time and servo voltage have a secondary effect.Table 10

shows that a greater discharge on time and arc on time, and increase of workpiece height leads to a wider groove. In addition, machined groove width is posi-tively correlated to average gap voltage, and it is nega-tively related to machining speed. If the gap voltage is reduced and the machining speed is increased, the machined groove width will be reduced. If Eq. (5) is rewritten as: G¼VDKFqðT 2 onð1 rÞ þ A2onðr=2ÞÞg u0HF ; ð11Þ

then a quantitative relationship for machined groove width is obtained. The workpiece height, discharge eﬃciency and material (that is SDE) are ﬁxed during

Table 8

Experimental level settings

Control factor Level Unit

1 2 3

Thickness H 10 50 mm

Discharge on time Ton 3 5 7 0.1 ls (1–9 step) Discharge off time Toff 20 35 50 1 ls (8–50 step) Arc on time Aon 2 3 4 0.1 ls (1–5 step) Arc off time Aoff 20 35 50 1 ls (9–50 step) Servo voltage Sv 40 55 70 V (35–70 V)

Wire speed Ws 5 7 10 1–16 m/min (0–15 step) Flushing pressure Fw 3 5 7 0–20 kg/cm2(0–7 step)

Table 9

Inﬂuences of the machining parameters on machining characteristics Machining

characteristic

H Ton Toﬀ Aon Aoﬀ Sv Ws Fw

Abnormal ratio tt q t tt Groove width tt tt t t Machining speed tt t q t Surface roughness tt Spark frequency tt tt tt Discharge eﬃciency tt tt

tt, most significant factor; t, significant factor; q, less significant factor.

Table 10

Variation of machining characteristics varied with respect to signiﬁcant machining parameters

Abnormal ratio Groove width Machining speed Surface roughness Spark frequency Discharge eﬃciency

H % % &

Ton % % % % &

Toﬀ & &

Aon %

Aoﬀ & &

Sv & % & & &

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machining, while other physical quantities can be mea-sured on line, hence the variation of machining groove width can be estimated on line.

When estimating the variation of machined groove width on line is wanted, a mathematical model relating discharge eﬃciency g and discharge on time and servo voltage is needed, and the simplest approach is to establish this relationship by regression analysis. By postulating the quadratic formfunctional relationship, the model can be expressed as:

g¼ X b þ e ð12Þ

where X is matrix of [X2

1 X22 X1X2 X1 X2 1], where

X1 and X2 are related to signiﬁcant factors. b¼

ðXT_XÞ1_XT_{Y ,} _X

1¼ logðTonÞ=maxðlogðTonÞÞ, X2¼

logðVgÞ=maxðlogðVgÞÞ, and 3 Ton 9, 30 Vg 80.

Hence 0:5 X1 1, 0:776 X2 1.

After curve ﬁtting of experimental data yields g¼ 1:5682X₁2þ 3:18546X₂2 2:7395X1X2

2:0132X1 4:3356X2þ 5:2435 ð13Þ

The correlation coefficient R that stands for the goodness of fit is found to be 0.9954. This high corre-lation coefficient value of almost 1 indicates that the above mathematical expression relating discharge efficiency, discharge on time and servo voltage, estab-lished through regression is highly representative and acceptable.

4.2. Analysis of a single discharge

The surface of a WEDM’d workpiece is formed by the pits resulting frommany discharges. This surface is not smooth and is usually quantiﬁed by surface rough-ness. The surface roughness is mainly determined by the peak current value; the larger the peak current value, the larger the surface roughness.

Fromthe perspective of a single discharge during the machining process, let the erosion diameter of each sin-gle discharge be D, the rate of erosion toward the inside of workpiece be Se, and the average temperature

at the single discharge instant be denoted by hh. The workpiece surface roughness is positively correlated with Se. Referring to Eq. (6), the following equation

can be derived by analogy h h u0 kqc DSe 1=2 ¼ C3 ð14Þ

Rearranging the above equation, the single discharge erosion rate can be written as

Se kqc D hh u0 2 ð15Þ If WW denotes the power of a single discharge, it can be expressed as the energy provided of a single dis-charge divided by the total pulse time which is twice

that of discharge time. That is:

W

W ¼KVDTon

2 ð16Þ

For a single normal discharge, the physical quan-tities related to average temperature at discharge instant are power of a single discharge, speciﬁc discharge energy, thermal properties of material, discharge eﬃciency, and the erosion diameter of a sin-gle discharge. Similar to Eq. (8), a dimensionless relationship is obtained by analogy.

1 h h W Wu0g kqcD 1=2 ¼ C4 ð17Þ Hence h h WWu0g kqcD 1=2 ð18Þ

Substituting Eq. (18) into Eq. (15) yields

Se W Wg u0D2 ð19Þ

Then the rate of material removal (volume/time) is

SeD2 W Wg u0 ð20Þ

The eﬃciency of material removal deﬁning as the volume of material removal per unit energy input (volume/energy) is SeD2 W W g u0 ð21Þ

It is well known fromexperience that an increase in discharge on time results in a rise of machining speed or material removal. However, it has been discussed in Section 3.2 that the greater the discharge on time, the smaller the discharge efficiency. Hence, with the aid of Eq. (20), it can be concluded that the amount of the decrease of discharge efficiency is less than the increase of WW due to the increase of the discharge on time. It should also be noted that while the rate of material removal is increased, the efficiency of material removal will decrease when discharge on time is increased in rough machining as depicted by Eqs. (20) and (21). Surface roughness is positively correlated with the sin-gle discharge erosion rate Se. Again, It is clear from

Eq. (19) that roughness of the machined surface is increased with the rate of energy provided by single discharge and discharge eﬃciency. But it inversely var-ies with SDE and the erosion diameter of a single dis-charge. Under the same machining conditions, the surface roughness will improve when there is a greater SDE, and vice versa.

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5. Conclusion

1. A new concept of specific discharge energy (SDE) is presented in the paper. It is found that this quantity is a material property in WEDM. The relative relationship of SDE for different materials is fixed as long as these materials are machined under the same machining conditions. Materials having similar value of SDE display very similar machining char-acteristics if they are machined under the same machining condition.

2. By means of dimensional analysis of SDE, a quanti-tative relationship between the machining para-meters and gap width in WEDM is obtained. This relationship will be extremely helpful to the develop-ment of new servo control strategy.

3. Under steady machining process, the smaller dis-charge gap results in higher disdis-charge eﬃciency. The shorter the normal discharge on time, the higher the discharge eﬃciency.

4. The material removal is increased but the eﬃciency of material removal (i.e. volume of material removal per unit energy input) is decreased with the increase of discharge on time. Under the same machining conditions, the surface roughness will become better when there is a greater SDE, and vice versa.

5. Finally, using the characteristics of SDE, determi-nation of parameter settings for diﬀerent materials can be greatly simpliﬁed, and this work is under way.

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